Transpiration cooling is an innovative cooling concept where a coolant is injected through a porous ceramic matrix composite (CMC) material into a hot gas flow. This setting is modeled by a two-domain approach coupling two models for the hot gas domain and the porous medium to each other by coupling conditions imposed at the interface. For this purpose, appropriate coupling conditions, in particular accounting for local mass injection, are developed. To verify the feasibility of the two-domain approach numerical simulations in 3D are performed for two different application scenarios: a subsonic thrust chamber and a supersonic nozzle.